求解微分方程通解的详细过程

2025-02-24 09:39:54
推荐回答(1个)
回答1:

y'=(2/x)y + x^2
let
u=y/x^2
du/dx = (-2y/x^3 + y'/x^2)
= -2u/x +y'/x^2
y'= x^2.du/dx + 2xu
/

y'=(2/x)y + x^2
x^2.du/dx + 2xu = 2xu + x^2
du/dx = 1
u= x+C
y/x^2 = x+C
y= x^3 +Cx^2